Hybrid Policy

In our narrative example we slowly moved from TAC to ITQ, then to ITQ + MPA which we can handily show in a Pareto plot:

Now rather than having to come up with the policy ourselves we could simply increase the number of parameters to search in and look for a general, hybrid policy; very much like in the one population case.

The advantage is that the computer searches for the policy itself. The disadvantage is that it takes a lot longer since the dimensions have increased. This is particularly so when we are building an entire pareto front rather than just looking to maximise a score.

This particular problem is 14-dimensional:

Parameters Meaning
Yearly Quota Amount of quota given to each boat, large and small
Season Length Maximum number of days before fishery is closed
\(\text{MPA}_x\) X coordinate of top left MPA corner on Map
\(\text{MPA}_y\) Y coordinate of top left MPA corner on Map
MPA height Heigth (in cells) of the MPA
MPA width Width (in cells) of the MPA
MPA duration Number of days within a year where the MPA is active
MPA start date Day of the year when MPA is activated
\(\text{EEZ}_x\) X coordinate of top left EEZ corner on Map
\(\text{EEZ}_y\) Y coordinate of top left EEZ corner on Map
EEZ height Heigth (in cells) of the EEZ
EEZ width Width (in cells) of the EEZ
EEZ duration Number of days within a year where the EEZ is active
EEZ start date Day of the year when EEZ is activated

Where by MPA I mean in this case an actual MPA where no-one is allowed and for EEZ I mean an area where small fishers can go but large fishers can’t.

We run the genetic algorithm for 40 generations and we can super-impose the new pareto front on top of the old ones:

As you can see there is a big improvement in cumulative landings. However even after 40 generations some of the best policies for small fishermen discovered through the simpler “MPA+ITQ” search have not been discovered yet. This is normal when the space is so large and it’s only a matter of running the algorithm for longer.

In general however, we can improve cumulative landings by a lot.
It’s interesting to pick one solution in particular with expected scores

Small Fishermen Income Landings
22,501,728 $ 27,312,766 kg

The way it works is that it establishes a fixed season length of 280 days. It also creates an EEZ much larger than in the original MPA+ITQ setting:

Parameters Value
\(\text{EEZ}_x\) 9
\(\text{EEZ}_y\) 7
EEZ height 31
EEZ width 35

However the key “innovation” is that the EEZ is only valid for approximately 190 days, leaving 80 days a year where large boats can exploit it freely.

Parameters Value
EEZ duration 186 days
EEZ start date 13 January

This is a pretty smart policy for a two reasons:

  1. It disperses the effort of large boats over a wider area. We know from previous simulations that when the EEZ is year-round large boats fish the line. However the logistic biology performs better (that is, has higher recruits) when boats do not exploit any one area exclusively. By building a large EEZ and then opening it towards the end of the season we make sure large boats fish a bit the line and a bit inside as well.
  2. It gives a head-start for small boats where they can exploit the area just next to port. This way they can make money, increase their reservation price for quotas and disincentivate the large boats to fish too close to port when the eez protection ends (since by then those areas are also half-depleted by the small fishers).

Quotas are set to 14,674kg per boat, which is higher than the 11,820kg that was optimal when we had MPA + ITQ alone. This is because the ITQs here stop being a tool to enforce fishing limits and become almost exclusively a tool for redistribution of income from large boats to small ones. This is because the quotas are rarely ever binding: landings are always a bit below the total available quotas. This can be seen in the next plot by looking at the red line which represents the total quota available:

The quota is set low enough as to be expensive and to force large boats to buy from small vessels and in fact yearly quota prices average at about 34% of ex vessel price:

Most of the biomass control is done by the EEZ and the fixed season length.

The optimiser also turns off the MPA. That is it sets its starting date in December (which is after the season as a whole ends). This is also a result that is common from our optimiser where pointless parameters are dropped. It doesn’t have to be necessarilly the case, at which point we would need to employ complexity control, but it is now.

Here’s how it looks like in practice. You can see the large boats raiding the EEZ for the first week of the year and the remaining 80 days of season.